Elements of the Theory of Markov Processes and Their ApplicationsGraduate-level text and reference in probability, with numerous scientific applications. Nonmeasure-theoretic introduction to theory of Markov processes and to mathematical models based on the theory. Appendixes. Bibliographies. 1960 edition. |
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Page 198
... tion the occurrence of phenotypic delay . This effect is very important in the study of mutation processes , since the appearance of the charac- teristic which differentiates normal and mutant forms , termed pheno- typic expression ...
... tion the occurrence of phenotypic delay . This effect is very important in the study of mutation processes , since the appearance of the charac- teristic which differentiates normal and mutant forms , termed pheno- typic expression ...
Page 339
... tion between the densities at n points in the field , since it is this correla- tion function which is of primary interest in the astrophysical problem . Let the vector t = ( t ( 1 ) , . . . , t ( n ) ) denote the position of a point in ...
... tion between the densities at n points in the field , since it is this correla- tion function which is of primary interest in the astrophysical problem . Let the vector t = ( t ( 1 ) , . . . , t ( n ) ) denote the position of a point in ...
Page 415
... tion of Y ( t ) : B * ( ) = lim P { Y ( t ) ≤ § | X ( t ) = x } t - 00 x = 0 , 1 , m - 1 The stochastic process described is in general non - Markovian ; how- ever , it may be considered as a Markov process if the state of the system ...
... tion of Y ( t ) : B * ( ) = lim P { Y ( t ) ≤ § | X ( t ) = x } t - 00 x = 0 , 1 , m - 1 The stochastic process described is in general non - Markovian ; how- ever , it may be considered as a Markov process if the state of the system ...
Contents
Introduction | 1 |
Processes Discrete in Space and Time | 9 |
Processes Discrete in Space and Continuous in Time | 57 |
Copyright | |
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Other editions - View all
Elements of the Theory of Markov Processes and Their Applications A. T. Bharucha-Reid Limited preview - 2012 |
Elements of the Theory of Markov Processes and Their Applications Albert T. Bharucha-Reid Limited preview - 1997 |
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absorber applications assume assumptions asymptotic birth process birth-and-death process boundary branching processes cascade process cascade theory coefficient collision consider counter defined denote the number denote the probability deterministic differential equation diffusion equations diffusion processes discrete branching process distribution function E₁ electron-photon cascades energy epidemic exists expression Feller finite functional equation given Hence initial condition integral equation interval 0,t ionization Kolmogorov equations Laplace transform Let the random machine Markov chain Markov processes Math mathematical matrix Mellin transform method Monte Carlo methods neutron nonnegative nucleon number of individuals o(At obtain P₁ photon Poisson process population probability distribution problem Proc product density queueing system r₁ radiation Ramakrishnan random variable random variable X(t random walk recurrent satisfies sequence Statist stochastic model Stochastic Processes t₁ t₂ Takács tion transition probabilities X₁ zero дх